Biomedical parameter probabilistic estimation method and apparatus

ABSTRACT

A probabilistic digital signal processor is described. Initial probability distribution functions are input to a dynamic state-space model, which operates on state and/or model probability distribution functions to generate a prior probability distribution function, which is input to a probabilistic updater. The probabilistic updater integrates sensor data with the prior to generate a posterior probability distribution function passed (1) to a probabilistic sampler, which estimates one or more parameters using the posterior, which is output or re-sampled in an iterative algorithm or (2) iteratively to the dynamic state-space model. For example, the probabilistic processor operates using a physical model on data from a mechanical system or a medical meter or instrument, such as an electrocardiogram. Output of the physical model yields an enhanced output of the original data, an output to a second physical parameter not output by the medical meter, or a prediction, such as an arrhythmia warning.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims:

-   -   priority to U.S. patent application Ser. No. 12/796,512, filed        Jun. 8, 2010, which claims priority to U.S. patent application        Ser. No. 12/640,278, filed Dec. 17, 2009, which under 35 U.S.C.        120 claims benefit of U.S. provisional patent application No.        61/171,802, filed Apr. 22, 2009,    -   benefit of U.S. provisional patent application No. 61/366,437        filed Jul. 21, 2010;    -   benefit of U.S. provisional patent application No. 61/372,190        filed Aug. 10, 2010; and    -   benefit of U.S. provisional patent application No. 61/373,809        filed Aug. 14, 2010,    -   all of which are incorporated herein in their entirety by this        reference thereto.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The U.S. Government may have certain rights to this invention pursuantto Contract Number IIP-0839734 awarded by the National ScienceFoundation.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates generally to apparatus and methods forprocessing and/or representing sensor data, such as mechanical ormedical sensor data.

Discussion of the Related Art

Mechanical devices and biomedical monitoring devices such as pulseoximeters, glucose sensors, electrocardiograms, capnometers, fetalmonitors, electromyograms, electroencephalograms, and ultrasounds aresensitive to noise and artifacts. Typical sources of noise and artifactsinclude baseline wander, electrode-motion artifacts, physiologicalartifacts, high-frequency noise, and external interference. Someartifacts can resemble real processes, such as ectopic beats, and cannotbe removed reliably by simple filters; however, these are removable bythe techniques taught herein. In addition, mechanical devices andbiomedical monitoring devices address a limited number of parameters. Itwould be desirable to expand the number of parameters measured, such asto additional biomedical state parameters.

Patents related to the current invention are summarized herein.

Mechanical Systems

Several reports of diagnostics and prognostics applied to mechanicalsystems have been reported.

Vibrational Analysis

R. Klein “Method and System for Diagnostics and Prognostics of aMechanical System”, U.S. Pat. No. 7,027,953 B2 (Apr. 11, 2006) describesa vibrational analysis system for diagnosis of health of a mechanicalsystem by reference to vibration signature data from multiple domains,which aggregates several features applicable to a desired fault fortrend analysis of the health of the mechanical system.

Intelligent System

S. Patel, et. al. “Process and System for Developing PredictiveDiagnostic Algorithms in a Machine”, U.S. Pat. No. 6,405,108 B1 (Jun.11, 2002) describe a process for developing an algorithm for predictingfailures in a system, such as a locomotive, comprising conducting afailure mode analysis to identify a subsystem, collecting expert data onthe subsystem, and generating a predicting signal for identifyingfailure modes, where the system uses external variables that affect thepredictive accuracy of the system.

C. Bjornson, “Apparatus and Method for Monitoring and Maintaining PlantEquipment”, U.S. Pat. No. 6,505,145 B1 (Jan. 11, 2003) describes acomputer system that implements a process for gathering, synthesizing,and analyzing data related to a pump and/or a seal, in which data aregathered, the data is synthesized and analyzed, a root cause isdetermined, and the system suggests a corrective action.

C. Bjornson, “Apparatus and Method for Monitoring and Maintaining PlantEquipment”, U.S. Pat. No. 6,728,660 B2 (Apr. 27, 2004) describes acomputer system that implements a process for gathering, synthesizing,and analyzing data related to a pump and/or a seal, in which data aregathered, the data is synthesized and analyzed, and a root cause isdetermined to allow a non-specialist to properly identify and diagnose afailure associated with a mechanical seal and pump.

K. Pattipatti, et. al. “Intelligent Model-Based Diagnostics for SystemMonitoring, Diagnosis and Maintenance”, U.S. Pat. No. 7,536,277 B2 (May19, 2009) and K. Pattipatti, et. al. “Intelligent Model-BasedDiagnostics for System Monitoring, Diagnosis and Maintenance”, U.S. Pat.No. 7,260,501 B2 (Aug. 21, 2007) both describe systems and methods formonitoring, diagnosing, and for condition-based maintenance of amechanical system, where model-based diagnostic methodologies combine orintegrate analytical models and graph-based dependency models to enhancediagnostic performance.

Inferred Data

R. Tryon, et. al. “Method and Apparatus for Predicting Failure in aSystem”, U.S. Pat. No. 7,006,947 B2 (Feb. 28, 2006) describe a methodand apparatus for predicting system failure or reliability using acomputer implemented model relying on probabilistic analysis, where themodel uses data obtained from references and data inferred from acquireddata. More specifically, the method and apparatus uses a pre-selectedprobabilistic model operating on a specific load to the system while thesystem is under operation.

Virtual Prototyping

R. Tryon, et. al. “Method and Apparatus for Predicting Failure of aComponent”, U.S. Pat. No. 7,016,825 B1 (Mar. 21, 2006) describe a methodand apparatus for predicting component failure using a probabilisticmodel of a material's microstructural-based response to fatigue usingvirtual prototyping, where the virtual prototyping simulates grain size,grain orientation, and micro-applied stress in fatigue of component.

R. Tryon, et. al. “Method and Apparatus for Predicting Failure of aComponent, and for Determining a Grain Orientation Factor for aMaterial”, U.S. Pat. No. 7,480,601 B2 (Jan. 20, 2009) describe a methodand apparatus for predicting component failure using a probabilisticmodel of a material's microstructural-based response to fatigue using acomputer simulation of multiple incarnations of real material behavioror virtual prototyping.

Medical Systems

Several reports of systems applied to biomedical systems have beenreported.

Lung Volume

M. Sackner, et. al. “Systems and Methods for Respiratory EventDetection”, U.S. Patent application no. 2008/0082018 A1 (Apr. 3, 2008)describe a system and method of processing respiratory signals frominductive plethysmographic sensors in an ambulatory setting that filtersfor artifact rejection to improve calibration of sensor data and toproduce output indicative of lung volume.

Pulse Oximeter

J. Scharf, et. al. “Separating Motion from Cardiac Signals Using SecondOrder Derivative of the Photo-Plethysmograph and Fast FourierTransforms”, U.S. Pat. No. 7,020,507 B2 (Mar. 28, 2006) describes theuse of filtering photo-plethysmograph data in the time domain to removemotion artifacts.

M. Diab, et. al. “Plethysmograph Pulse Recognition Processor”, U.S. Pat.No. 6,463,311 B1 (Oct. 8, 2002) describe an intelligent, rule-basedprocessor for recognition of individual pulses in a pulseoximeter-derived photo-plethysmograph waveform operating using a firstphase to detect candidate pulses and a second phase applying aplethysmograph model to the candidate pulses resulting in period andsignal strength of each pulse along with pulse density.

C. Baker, et. al. “Method and Apparatus for Estimating PhysiologicalParameters Using Model-Based Adaptive Filtering”, U.S. Pat. No.5,853,364 (Dec. 29, 1998) describe a method and apparatus for processingpulse oximeter data taking into account physical limitations usingmathematical models to estimate physiological parameters.

Cardiac

J. McNames, et. al. “Method, System, and Apparatus for CardiovascularSignal Analysis, Modeling, and Monitoring”, U.S. patent applicationpublication no. 2009/0069647 A1 (Mar. 12, 2009) describe a method andapparatus to monitor arterial blood pressure, pulse oximetry, andintracranial pressure to yield heart rate, respiratory rate, and pulsepressure variation using a statistical state-space model ofcardiovascular signals and a generalized Kalman filter to simultaneouslyestimate and track the cardiovascular parameters of interest.

M. Sackner, et. al. “Method and System for Extracting Cardiac Parametersfrom Plethysmograph Signals”, U.S. patent application publication no.2008/0027341 A1 (Jan. 31, 2008) describe a method and system forextracting cardiac parameters from ambulatory plethysmographic signal todetermine ventricular wall motion.

Hemorrhage

P. Cox, et. al. “Methods and Systems for Non-Invasive InternalHemorrhage Detection”, International Publication no. WO 2008/055173 A2(May 8, 2008) describe a method and system for detecting internalhemorrhaging using a probabilistic network operating on data from anelectrocardiogram, a photoplethysmogram, and oxygen, respiratory, skintemperature, and blood pressure measurements to determine if the personhas internal hemorrhaging.

Disease Detection

V. Karlov, et. al. “Diagnosing Inapparent Diseases From Common ClinicalTests Using Bayesian Analysis”, U.S. patent application publication no.2009/0024332 A1 (Jan. 22, 2009) describe a system and method ofdiagnosing or screening for diseases using a Bayesian probabilityestimation technique on a database of clinical data.

Statement of the Problem

Mechanical and biomedical sensors are typically influenced by multiplesources of contaminating signals that often overlap the frequency of thesignal of interest, making it difficult, if not impossible, to applyconventional filtering. Severe artifacts such as occasional signaldropouts due to sensor movement or large periodic artifacts are alsodifficult to filter in real time. Biological sensor hardware can beequipped with a computer comprising software for post-processing dataand reducing or rejecting noise and artifacts. Current filteringtechniques typically use some knowledge of the expected frequencies ofinterest where the sought-after physiological information should befound.

Adaptive filtering has been used to attenuate artifacts in pulseoximeter signals corrupted with overlapping frequency noise bands byestimating the magnitude of noise caused by patient motion and otherartifacts and canceling its contribution from pulse oximeter signalsduring patient movement. Such a time correlation method relies on aseries of assumptions and approximations to the expected signal, noise,and artifact spectra, which compromises accuracy, reliability, andgeneral applicability.

Filtering techniques based on Kalman and extended Kalman techniquesoffer advantages over conventional methods and work well for filteringlinear systems or systems with small nonlinearities and Gaussian noise.These filters, however, are not adequate for filtering highly nonlinearsystems and non-Gaussian/non-stationary noise. Therefore, obtainingreliable biomedical signals continue to present problems, particularlywhen measurements are made in mobile, ambulatory, and physically activepatients.

Existing data processing techniques, including adaptive noisecancellation filters, are unable to extract information that is hiddenor embedded in biomedical signals and also discard some potentiallyvaluable information.

Existing medical sensors sense a narrow spectrum of medical parametersand states. What is needed is a system readily expanding the number ofbiomedical states determined.

A method or apparatus for extracting additional useful information froma mechanical sensor in a mechanical system, a biomedical system, and/ora system component or sub-component is needed to provide usersadditional and/or clearer information.

SUMMARY OF THE INVENTION

The invention comprises use of a probabilistic model to extract, filter,estimate and/or add additional information about a system based on datafrom a sensor.

DESCRIPTION OF THE FIGURES

A more complete understanding of the present invention is derived byreferring to the detailed description and claims when considered inconnection with the Figures, wherein like reference numbers refer tosimilar items throughout the Figures.

FIG. 1 illustrates operation of the intelligent data extractionalgorithm on a biomedical apparatus;

FIG. 2 provides a block diagram of a data processor;

FIG. 3 is a flow diagram of a probabilistic digital signal processor;

FIG. 4 illustrates a dual estimator;

FIG. 5 expands the dual estimator;

FIG. 6 illustrates state and model parameter estimators;

FIG. 7 provides inputs and internal operation of a dynamic state-spacemodel;

FIG. 8 is a flow chart showing the components of a hemodynamics dynamicstate-space model;

FIG. 9 is a chart showing input sensor data, FIG. 9A; processed outputdata of heart rate, FIG. 9B; stroke volume, FIG. 9C; cardiac output,FIG. 9D; oxygen, FIG. 9E; and pressure, FIG. 9F from a data processorconfigured to process pulse oximetry data;

FIG. 10 is a chart showing input sensor data, FIG. 10A, and processedoutput data, FIGS. 10A-10E, from a data processor configured to processpulse oximetry data under a low blood perfusion condition;

FIG. 11 is a flow chart showing the components of a electrocardiographdynamic state-space model;

FIG. 12 is a chart showing noisy non-stationary ECG sensor data input,FIG. 12A and FIG. 12B and processed heart rate and ECG output, FIG. 12Aand FIG. 12B, for a data processor configured to process ECG sensordata;

FIG. 13A and FIG. 13B are charts showing input ECG sensor data andcomparing output data from a data processor according to the presentinvention with output data generating using a Savitzky-Golay FIR dataprocessing algorithm; and

FIG. 14 provides a flowchart of dynamic state-space model diagnosticsused as prognosis and control.

DETAILED DESCRIPTION OF THE INVENTION

The invention comprises use of a method, a system, and/or an apparatususing a probabilistic model for monitoring and/or estimating a parameterusing a sensor.

The system applies to the mechanical and medical fields. Herein, forclarity the system is applied to biomedical devices, though the systemconcepts apply to mechanical apparatus.

In one embodiment, an intelligent data extraction algorithm (IDEA) isused in a system, which combines a dynamic state-space model with aprobabilistic digital signal processor to estimate a parameter, such asa biomedical parameter. Initial probability distribution functions areinput to a dynamic state-space model, which iteratively operates onprobability distribution functions, such as state and model probabilitydistribution functions, to generate a prior probability distributionfunction, which is input into a probabilistic updater. The probabilisticupdater integrates sensor data with the prior probability distributionfunction to generate a posterior probability distribution functionpassed to a probabilistic sampler, which estimates one or moreparameters using the posterior, which is output or re-sampled and usedas an input to the dynamic state-space model in the iterative algorithm.In various embodiments, the probabilistic data signal processor is usedto filter output and/or estimate a value of a new physiologicalparameter from a biomedical device using appropriate physical models,which optionally include biomedical, chemical, electrical, optical,mechanical, and/or fluid based models. For clarity, examples of heartand cardiovascular medical devices are provided.

In various embodiments, the probabilistic digital signal processorcomprises one or more of a dynamic state-space model, a dual or jointupdater, and/or a probabilistic sampler, which process input data, suchas sensor data and generates an output. Preferably, the probabilisticdigital signal processor (1) iteratively processes the data and/or (2)uses a physical model in processing the input data.

The probabilistic digital signal processor optionally:

-   -   operates on or in conjunction with a sensor in a mechanical        system;    -   operates using data from a medical meter, where the medical        meter yields a first physical parameter from raw data, to        generate a second physical parameter not output by the medical        meter;    -   operates on discrete/non-probabilistic input data, such as from        a mechanical device or a medical device to generate a        probabilistic output function;    -   iteratively circulates or circulates a dynamic probability        distribution function through at least two of the dynamic        state-space model, the dual or joint updater, and/or the        probabilistic sampler;    -   fuses or combines output from multiple sensors, such as two or        more medical devices; and    -   prognosticates probability of future events.

To facilitate description of the probabilistic digital signal processor,a first non-limiting example of a hemodynamics process model isprovided. In this example, the probabilistic digital signal processor isprovided:

-   -   raw sensor data, such as current, voltage, and/or resistance;        and/or    -   output from a medical device to a first physical parameter.

In this example, the medical device is a pulse oximeter and the firstphysical parameter from the pulse oximeter provided as input to theprobabilistic digital signal processor is one or more of:

-   -   raw data;    -   heart rate; and/or    -   blood oxygen saturation.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameter togenerate a second physical parameter, where the second physicalparameter is not the first physical parameter. For example, the outputof the probabilistic digital signal processor when provided with thepulse oximeter data is one or more of:

-   -   a heart stroke volume;    -   a cardiac output flow rate;    -   an aortic blood pressure; and/or    -   a radial blood pressure.

Optionally, the output from the probabilistic model is an updated, errorfiltered, and/or, a smoothed version of the original input data, such asa smoothed blood oxygen saturation percentage as a function of time. Thehemodynamics model is further described, infra.

To facilitate description of the probabilistic digital signal processor,a second non-limiting example of an electrocardiograph process model isprovided. In this example, the probabilistic digital signal processor isprovided:

-   -   raw sensor data, such as intensity, an electrical current,        and/or a voltage; and/or    -   output from a medical device, such as an electrocardiogram, to a        first physical parameter.

In this example, the medical device is a electrocardiograph and thefirst physical parameter from the electrocardiograph system provided asinput to the probabilistic digital signal processor is one or more of:

-   -   raw data; and/or    -   an electrocardiogram.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameter togenerate a second physical parameter or an indicator, where the secondphysical parameter is not the first physical parameter. For example, theoutput of the probabilistic digital signal processor when provided withthe electrocardiogram or raw data is one or more of:

-   -   an arrhythmia detection;    -   an ischemia warning; and/or    -   a heart attack prediction.

Optionally, the output from the probabilistic model is an updated, errorfiltered, or smoothed version of the original input data. For example,the probabilistic processor uses a physical model where the output ofthe model processes low signal-to-noise ratio events to yield an earlywarning of any of the arrhythmia detection, the ischemia warning, and/orthe heart attack prediction. The electrocardiograph model is furtherdescribed, infra.

Deterministic vs. Probabilistic Models

Typically, computer-based systems use a mapping between observedsymptoms of failure and the equipment where the mapping is built usingdeterministic techniques. The mapping typically takes the form of alook-up table, a symptom-problem matrix, trend analysis, and productionrules. In stark contrast, alternatively probabilistic models are used toanalyze a system. An example of a probabilistic model, referred toherein as an intelligent data extraction system is provided, infra.

Intelligent Data Extraction System

Referring now to FIG. 1, an algorithm based intelligent data extractionsystem 100 is illustrated. The intelligent data extraction system 100uses a controller 110 to control a sensor 120. The sensor 120 is used tomeasure a parameter and/or is incorporated into a biomedical apparatus130. Optionally, the controller 110 additionally controls the medicalapparatus and/or is built into the biomedical apparatus 130. In oneembodiment, the controller 110 comprises: a microprocessor in a computeror computer system, an embedded processor, and/or an embedded device.The sensor 120 provides readings to a data processor or a probabilisticdigital signal processor 200, which provides feedback to the controller110 and/or provides output 150.

Herein, to enhance understanding and for clarity of presentation,non-limiting examples of an intelligent data extraction system operatingon a hemodynamics biomedical devices are used to illustrate methods,systems, and apparatus described herein. Generally, the methods,systems, and apparatus described herein extend to any apparatus having amoveable part and/or to any medical device. Examples of the dynamicstate-space model with a probabilistic digital signal processor used toestimate parameters of additional biomedical systems are provided afterthe details of the processing engine are presented.

Still referring to FIG. 1, in a pulse oximeter example the controller110 controls a sensor 120 in the pulse oximeter apparatus 130. Thesensor 120 provides readings, such as a spectral reading to theprobabilistic digital signal processor 200, which is preferably aprobability based data processor. The probabilistic digital signalprocessor 200 optionally operates on the input data or provides feedbackto the controller 110, such as state of the patient, as part of a loop,iterative loop, time series analysis, and/or generates the output 150,such as a smoothed biomedical state parameter or a new biomedical stateparameter. For clarity, the pulse oximeter apparatus is usedrepetitively herein as an example of the biomedical apparatus 130 uponwhich the intelligent data extraction system 100 operates. Theprobabilistic digital signal processor 200 is further described, infra.

Data Processor

Referring now to FIG. 2, the probabilistic digital signal processor 200of the intelligent data extraction system 100 is further described.Generally, the data processor includes a dynamic state-space model 210(DSSM) and a probabilistic updater 220 that iteratively or sequentiallyoperate on sensor data 122 from the sensor 120. The probabilisticupdater 220 outputs a probability distribution function to a parameterupdater or a probabilistic sampler 230, which generates one or moreparameters, such as an estimated diagnostic parameter, which is sent tothe controller 110, is used as part of an iterative loop as input to thedynamic state-space model 210, and/or is a basis of the output 150. Thedynamic state-space model 210 and probabilistic updater 220 are furtherdescribed, infra.

Referring now to FIG. 3, the probabilistic digital signal processor 200is further described. Generally, an initial probability distributionfunction (PDF) or a plurality of probability distribution functions(PDFs) 310 are input to the dynamic state-space model 210. In a process212, the dynamic state-space model 210 operates on the initialprobability distribution functions 310 to generate a prior probabilitydistribution function, hereinafter also referred to as a prior or as aprior PDF. For example, an initial state parameter 312 probabilitydistribution function and an initial model parameter 314 probabilitydistribution function are provided as initial inputs to the dynamicstate-space model 210. The dynamic state-space model 210 operates on theinitial state parameter 312 and/or initial model parameter 314 togenerate the prior probability distribution function, which is input tothe probabilistic updater 220. In a process 320, the probabilisticupdater 220 integrates sensor data, such as timed sensor data 122, byoperating on the sensor data and on the prior probabilistic distributionfunction to generate a posterior probability distribution function,herein also referred to as a posterior or as a posterior PDF. In aprocess 232, the probabilistic sampler 230 estimates one or moreparameters using the posterior probability distribution function. Theprobabilistic sampler 230 operates on the state and model parameterprobability distribution functions from the state and model parameterupdaters 224, 226, respectively or alternatively operates on the jointparameter probability distribution function and calculates an output.The output is optionally:

-   -   the state or joint parameter PDF, passed to the PDF resampler        520; and/or    -   output values resulting from an operation on the inputs to the        output 150 or output display or the 110 controller.

In one example, expectation values such as mean and a standard deviationof a state parameter are calculated from the state parameter PDF andoutput to the user, such as for diagnosis. In another example,expectation values, such as a mean value of state and model parameters,are calculated and then used in a model to output a more advanceddiagnostic or prognostic parameter. In a third example, expectationvalues are calculated on a PDF that is the result of an operation on thestate parameter PDF and/or model parameter PDF. Optionally, the outputis to the same parameter as the state parameter PDF or model parameterPDF. Other data, such as user-input data, is optionally used in theoutput operation. The estimated parameters of the probabilistic sampler230 are optionally used as a feedback to the dynamic state-space model210 or are used to estimate a biomedical parameter. The feedback to thedynamic state-space model 210 is also referred to as a new probabilityfunction or as a new PDF, which is/are updates of the initial stateparameter 312 and/or are updates of the initial model parameter 314.Again, for clarity, an example of an estimated parameter 232 is ameasurement of the heart/cardiovascular system, such as a heartbeatstroke volume.

Dual Estimator

In another embodiment, the probabilistic updater 220 of theprobabilistic digital signal processor 200 uses a dual or jointestimator 222. Referring now to FIG. 4, the joint estimator 222 or dualestimation process uses both a state parameter updater 224 and a modelparameter updater 226. Herein, for clarity, a dual estimator 222 isdescribed. However, the techniques and steps described herein for thedual estimator are additionally applicable to a joint estimator as thestate parameter and model parameter vector and/or matrix of the dualestimator are merely concatenated in a joint parameter vector and/or arejoined in a matrix in a joint estimator.

State Parameter Updater

A first computational model used in the probabilistic updater 220includes one or more state variables or state parameters, whichcorrespond to the parameter being estimated by the state parameterupdater 224. In the case of the hemodynamics monitoring apparatus, stateparameters include time, intensity, reflectance, and/or a pressure. Someor all state parameters are optionally chosen such that they representthe ‘true’ value of noisy timed sensor data. In this case, calculationof such a posterior state parameter PDF constitutes a noise filteringprocess and expectation values of the PDF optionally represent filteredsensor values and associated confidence intervals.

Model Parameter Updater

A second computational model used in the probabilistic updater 220includes one or more model parameters updated in the model parameterupdater 226. For example, in the case of the hemodynamics monitoringapparatus, model parameters include: a time interval, a heart rate, astroke volume, and/or a blood oxygenation percentage.

Hence, the dual estimator 222 optionally simultaneously or in aprocessing loop updates or calculates one or both of the stateparameters and model parameters. The probabilistic sampler 230 is usedto determine the estimated value for the biomedical parameter, which isoptionally calculated from a state parameter, a model parameter, or acombination of one or more of the state parameter and/or the modelparameter.

Referring still to FIGS. 3 and 4 and now referring to FIG. 5, a firstexample of the dual estimator 222 is described and placed into contextof the dynamic state-space model 210 and probabilistic sampler 230 ofthe probabilistic digital signal processor 200. The state parameterupdater 224 element of the dual estimator 222 optionally:

-   -   uses a sensor data integrator 320 operating on the prior PDF        being passed from the dynamic state-space model 210 and        optionally operates on new timed sensor data 122, to produce the        posterior PDF passed to the probabilistic sampler 230;    -   operates on current model parameters 510; and/or    -   in a process 520, the state parameter updater 224 optionally        re-samples a probability distribution function passed from the        probabilistic sampler 230 to form the new probability        distribution function passed to the dynamic state-space model        210.

In addition, in a process 530 the model parameter updater 226 optionallyintegrates new timed sensor data 122 with output from the probabilisticsampler 230 to form new input to the dynamic state-space model 210.

Referring now to FIG. 6, a second example of a dual estimator 222 isdescribed. In this example:

-   -   initial state parameter probability distribution functions 312        are passed to the dynamic state-space model 210; and/or    -   initial model parameter probability distribution functions 314        are passed to the dynamic state-space model 210;

Further, in this example:

-   -   a Bayesian rule applicator 322 is used as an algorithm in the        sensor data integrator 320;    -   a posterior distribution sample algorithm 522 is used as the        algorithm in the resampling of the PDF process 520; and    -   a supervised or unsupervised machine learning algorithm 532 is        used as the algorithm in the model parameter updater 530.        Filtering

In various embodiments, algorithms, data handling steps, and/ornumerical recipes are used in a number of the steps and/or processesherein. The inventor has determined that several algorithms areparticularly useful: sigma point Kalman filtering, sequential MonteCarlo filtering, and/or use of a sampler. In a first example, either thesigma point Kalman filtering or sequential Monte Carlo algorithms areused in generating the probability distribution function. In a secondexample, either the sigma point Kalman filtering or sequential MonteCarlo algorithms are used in the unsupervised machine learning 532 stepin the model parameter updater 530 to form an updated model parameter.The sigma point Kalman filtering, sequential Monte Carlo algorithms, anduse of a sampler are further described, infra.

Sigma Point Kalman Filter

Filtering techniques based on Kalman and extended Kalman techniquesoffer advantages over conventional methods and work well for filteringlinear systems or systems with small nonlinearities and Gaussian noise.These Kalman filters, however, are not optimum for filtering highlynonlinear systems and/or non-Gaussian/non-stationary noise. In starkcontrast, sigma point Kalman filters are well suited to data havingnonlinearities and non-Gaussian noise.

Herein, a sigma point Kalman filter (SPKF) refers to a filter using aset of weighted sigma-points that are deterministically calculated, suchas by using the mean and square-root decomposition, or an equivalent, ofthe covariance matrix of a probability distribution function to aboutcapture or completely capture at least the first and second ordermoments. The sigma-points are subsequently propagated in time throughthe dynamic state-space model 210 to generate a prior sigma-point set.Then, prior statistics are calculated using tractable functions of thepropagated sigma-points, weights, and new measurements.

Sigma point Kalman filter advantages and disadvantages are describedherein. A sigma point Kalman filter interprets a noisy measurement inthe context of a mathematical model describing the system andmeasurement dynamics. This gives the sigma point Kalman filter inherentsuperior performance to all ‘model-less’ methods, such as Wienerfiltering, wavelet de-noising, principal component analysis, independentcomponent analysis, nonlinear projective filtering, clustering methods,adaptive noise cancelling, and many others.

A sigma point Kalman filter is superior to the basic Kalman filter,extended Kalman filter, and related variants of the Kalman filters. Theextended Kalman filter propagates the random variable using a singlemeasure, usually the mean, and a first order Taylor expansion of thenonlinear dynamic state-space model 210. Conversely, a sigma pointKalman filter decomposes the random variable into distribution momentsand propagates those using the unmodified nonlinear dynamic state-spacemodel 210. As a result, the sigma point Kalman filter yields higheraccuracy with equal algorithm complexity, while also being easier toimplement in practice.

In the sigma-point formalism the probability distribution function isrepresented by a set of values called sigma points, those valuesrepresent the mean and other moments of the distribution which, wheninput into a given function, recovers the probability distributionfunction.

Sequential Monte Carlo

Sequential Monte Carlo (SMC) methods approximate the prior probabilitydistribution function through use of a set of weighted sample valueswithout making assumptions about its form. The samples are thenpropagated in time through the unmodified dynamic state-space model 210.The resulting samples are used to update the posterior via Bayes ruleand the latest noisy measurement or timed sensor data 122.

In the sequential Monte Carlo formalism the PDF is actually discretizedinto a collection of probability “particles” each representing a segmentof the probability density in the probability distribution function.

SPKF and SMC

In general, sequential Monte Carlo methods have analysis advantagescompared to the sigma point Kalman filters, but are more computationallyexpensive. However, the SPKF uses a sigma-point set, which is an exactrepresentation only for Gaussian probability distribution functions(PDFs). As a result, SPKFs lose accuracy when PDFs depart heavily fromthe Gaussian form, such as with bimodal, heavily-tailed, ornonstationary distributions. Hence, both the SMC and SPKF filters haveadvantages. However, either a SMC analysis or a SPKF is used topropagate the prior using the unmodified DSSM. Herein, generally when aSMC filter is used an SPKF filter is optionally used and vise-versa.

A SPKF or SMC algorithm is used to generate a reference signal in theform of a first probability distribution from the model's current(time=t) physiological state. The reference signal probabilitydistribution and a probability distribution generated from a measuredsignal from a sensor at a subsequent time (time=t+n) are convolutedusing Bayesian statistics to estimate the true value of the measuredphysiological parameter at time=t+n. The probability distributionfunction is optionally discrete or continuous. The probabilitydistribution function is optionally used to identify the probability ofeach value of an unidentified random variable, such as in a discretefunction, or the probability of the value falling within a particularinterval, such as in a continuous function.

Samplers

Probability distribution functions (PDFs) are optionally continuous ordiscrete. In the continuous case the probability distribution functionis represented by a function. In the discrete case, the variable spaceis binned into a series of discrete values. In both the continuous anddiscrete cases, probability distribution functions are generated byfirst decomposing the PDF into a set of samplers that are characteristicof the probability distribution function and then propagating thosesamplers via computations through the DSSM (prior generation) and sensordata integrator (posterior generation). Herein, a sampler is acombination of a value and label. The value is associated with thex-axis of the probability distribution function, which denotes state,model, or joint parameters. The label is associated with the y-axis ofthe probability distribution function, which denotes the probability.Examples of labels are: weight, frequency, or any arbitrary moment of agiven distribution, such as a first Gaussian moment. A powerful exampleof characteristic sampler use is decomposing the PDF into a series ofstate values with attached first Gaussian moment labels. This sum ofseveral Gaussian distributions with different values and moments usuallygives accurate approximations of the true probability distributionfunction.

Probabilistic Digital Signal Processor

As described, supra, in various embodiments, the probabilistic digitalsignal processor 200 comprises one or more of a dynamic state-spacemodel 210, a dual or joint estimator 222, and/or a probabilistic sampler230, which processes input data, such as sensor data 122 and generatesan output 150. Preferably, the probabilistic digital signal processor200 (1) iteratively processes the data and/or (2) uses a physical modelin processing the input data.

The probabilistic digital signal processor 200 optionally:

-   -   operates using data from a medical meter, where the medical        meter yields a first physical parameter from raw data, to        generate a second physical parameter not output by the medical        meter;    -   operates on discrete/non-probabilistic input data from a medical        device to generate a probabilistic output function;    -   iteratively circulates a probability distribution function        through at least two of the dynamic state-space model, the dual        or joint updater, and/or the probabilistic sampler;    -   fuses or combines output from multiple medical devices; and/or    -   prognosticates probability of future events.

A hemodynamics example of a probabilistic digital signal processor 200operating on data from a pulse oximeter is used to describe theseprocesses, infra.

Dynamic State-Space Model

The dynamic state-space model 210 is further described herein.

Referring now to FIG. 7, schematics of an exemplary dynamic state-spacemodel 210 (DSSM) used in the processing of data is provided. The dynamicstate-space model 210 typically and optionally includes a process model710 and/or an observation model 720. The process model 710, F, whichmathematically represents mechanical processes involved in generatingone or more biomedical parameters is measured by a sensor, such as asensor used to sense a mechanical component. The sensor data or processmodel 710 describes the state of the biomedical apparatus, output of thebiomedical apparatus, and/or state of the patient over time in terms ofstate parameters. This mathematical model optimally includesmathematical representations accounting for process noise 750, such asmechanically caused artifacts that may cause the sensor to produce adigital output that does not produce an accurate measurement for thebiomedical parameter being sensed. The dynamic state-space model 210also comprises an observational model 720, H, which mathematicallyrepresents processes involved in collecting sensor data measured by themechanical sensor. This mathematical model optimally includesmathematical representations accounting for observation noise producedby the sensor apparatus that may cause the sensor to produce a digitaloutput that does not produce an accurate measurement for a biomedicalparameter being sensed. Noise terms in the mathematical models are notrequired to be additive.

While the process and observation mathematical models 710, 720 areoptionally conceptualized as separate models, they are preferablyintegrated into a single mathematical model that describes processesthat produce a biomedical parameter and processes involved in sensingthe biomedical parameter. The integrated process and observation model,in turn, is integrated with a processing engine within an executableprogram stored in a data processor, which is configured to receivedigital data from one or more sensors and to output data to a displayand/or to another output format.

Still referring to FIG. 7, inputs into the dynamic state-space model 210include one or more of:

-   -   state parameters 730, such as the initial state parameter        probability distribution function 312 or the new PDF;    -   model parameters 740, such as the initial noise parameter        probability distribution function 314 or an updated model        parameter from the unsupervised machine learning module 532;    -   process noise 750; and/or    -   observation noise 760.        Hemodynamics Dynamic State-Space Model

A first non-limiting specific example is used to facilitateunderstanding of the dynamic state-space model 210. Referring now toFIG. 8, a hemodynamics dynamic state-space model 805 flow diagram ispresented. Generally, the hemodynamics dynamic state-space model 805 isan example of a dynamic state-space model 210. The hemodynamics dynamicstate-space model 805 combines sensor data 122, such as a spectralreadings of skin, with a physical parameter based probabilistic model.The hemodynamics dynamic state-space model 805 operates in conjunctionwith the probabilistic updater 220 to form an estimate ofheart/cardiovascular state parameters.

To facilitate description of the probabilistic digital signal processor,a non-limiting example of a hemodynamics process model is provided. Inthis example, the probabilistic digital signal processor is provided:

-   -   raw sensor data, such as current, voltage, and/or resistance;        and/or    -   a first physical parameter output from a medical device.

In this example, the medical device is a pulse oximeter collecting rawdata and the first physical parameter from the pulse oximeter providedas input to the probabilistic digital signal processor is one or moreof:

-   -   a heart rate; and/or    -   a blood oxygen saturation.

The probabilistic digital signal processor uses a physical model, suchas a probabilistic model, to operate on the first physical parameterand/or the raw data to generate a second physical parameter, where thesecond physical parameter is optionally not the first physicalparameter. For example, the output of the probabilistic digital signalprocessor using a physical hemodynamic models, when provided with thepulse oximeter data, is one or more of:

-   -   a heart stroke volume;    -   a cardiac output flow rate;    -   an aortic blood pressure; and/or    -   a radial blood pressure.

Optionally, the output from the probabilistic model is an updated, errorfiltered, and/or smoothed version of the original input data, such as asmoothed blood oxygen saturation percentage as a function of time.

Still referring to FIG. 8, to facilitate description of the hemodynamicsdynamic state-space model 805, a non-limiting example is provided. Inthis example, the hemodynamics dynamic state-space model 805 is furtherdescribed. The hemodynamics dynamic state-space model 805 preferablyincludes a hemodynamics process model 810 corresponding to the dynamicstate space model 210 process model 710. Further, the hemodynamicsdynamic state-space model 805 preferably includes a hemodynamicsobservation model 820 corresponding to the dynamic state space model 210observation model 720. The hemodynamics process model 810 andhemodynamics observation model 820 are further described, infra.

Still referring to FIG. 8, the hemodynamics process model 810 optionallyincludes one or more of a heart model 812, a vascular model 814, and/ora light scattering or a light absorbance model 816. The heart model 812is a physics based probabilistic model of the heart and movement ofblood in and/or from the heart. The vascular model 814 is a physicsbased probabilistic model of movement of blood in arteries, veins,and/or capillaries. The various models optionally share information. Forexample, blood flow or stroke volume exiting the heart in the heartmodel 812 is optionally an input to the arterial blood in the vascularmodel 814. The light scattering and/or absorbance model 816 relatesspectral information, such as from a pulse oximeter, to additionalhemodynamics dynamic state-space model parameters, such as heart rate(HR), stroke volume (SV), and/or whole-blood oxygen saturation (SpO₂) oroxyhemoglobin percentage.

Still referring to FIG. 8, the hemodynamics observation model 820optionally includes one or more of a sensor dynamics and noise model 822and/or a spectrometer signal transduction noise model 824. Each of thesensor dynamics and noise model 822 and the spectrometer signaltransduction noise model 824 are physics based probabilistic modelsrelated to noises associated with the instrumentation used to collectdata, environmental influences on the collected data, and/or noise dueto the human interaction with the instrumentation, such as movement ofthe sensor. As with the hemodynamics process model 810, the sub-modelsof the hemodynamics observation model 820 optionally share information.For instance, movement of the sensor noise is added to environmentalnoise. Optionally and preferably, the hemodynamics observation model 820shares information with and/provides information to the hemodynamicsprocess model 810.

The hemodynamics dynamic state-space model 805 receives inputs, such asone or more of:

-   -   hemodynamics state parameters 830;    -   hemodynamics model parameters 840;    -   hemodynamics process noise 850; and    -   hemodynamics observation noise 860.

Examples of hemodynamics state parameters 830, corresponding to stateparameters 730, include: radial pressure (P_(w)), aortic pressure(P_(ao)), time (t), a spectral intensity (l) or a related absorbancevalue, a reflectance or reflectance ratio, such as a red reflectance(R_(r)) or an infrared reflectance (R_(ir)), and/or a spectral intensityratio (I_(R)). Examples of hemodynamics model parameters 840,corresponding to the more generic model parameters 740, include: heartrate (HR), stroke volume (SV), and/or whole-blood oxygen saturation(SpO₂). In this example, the output of the hemodynamics dynamicstate-space model 805 is a prior probability distribution function withparameters of one or more of the input hemodynamics state parameters 830after operation on by the heart dynamics model 812, a static number,and/or a parameter not directly measured or output by the sensor data.For instance, an input data stream is optionally a pulse oximeteryielding spectral intensities, ratios of intensities, and a percentoxygen saturation. However, the output of the hemodynamics dynamicstate-space model is optionally a second physiological value, such as astroke volume of the heart, which is not measured by the inputbiomedical device.

The hemodynamics dynamic state-space model 805 optionally receivesinputs from one or more additional models, such as an irregular samplingmodel, which relates information collected at irregular or non-periodicintervals to the hemodynamics dynamic state-space model 805.

Generally, the hemodynamics dynamic state-space model 805 is an exampleof a dynamic state-space model 210, which operates in conjunction withthe probabilistic updater 220 to form an estimate of a heart stateparameter and/or a cardiovascular state parameter.

Generally, the output of the probabilistic signal processor 200optionally includes a measure of uncertainty, such as a confidenceinterval, a standard deviation, and/or a standard error. Optionally, theoutput of the probabilistic signal processor 200 includes:

-   -   a filtered or smoothed version of the parameter measured by the        medical meter; and/or    -   a probability function associated with a parameter not directly        measured by the medical meter.

EXAMPLE I

An example of a pulse oximeter with probabilistic data processing isprovided as an example of the hemodynamics dynamic state-space model805. The model is suitable for processing data from a pulse oximetermodel. In this example, particular equations are used to furtherdescribe the hemodynamics dynamic state-space model 805, but theequations are illustrative and non-limiting in nature.

Heart Model

An example of the heart model 812 is used to further described anexample of the hemodynamics dynamic state-space model 805. In thisexample, cardiac output is represented by equation 1,

$\begin{matrix}{{Q_{CO}(t)} = {{\overset{\_}{Q}}_{CO}{\sum\limits_{1}^{\delta}{a_{k}{\exp\lbrack \frac{- ( {t - b_{k}} )^{2}}{c_{k}^{2}} \rbrack}}}}} & (1)\end{matrix}$where cardiac output Q_(co)(t), is expressed as a function of heart rate(HR) and stroke volume (SV) and where Q_(co)=(HR×SV)/60. The valuesa_(k), b_(k), and c_(k) are adjusted to fit data on human cardiacoutput.Vascular Model

An example of the vascular model 814 of the hemodynamics state-spacemodel 805 is provided. The cardiac output function pumps blood into aWindkessel 3-element model of the vascular system including two statevariables: aortic pressure, P_(ao), and radial (Windkessel) pressure,P_(W), according to equations 2 and 3,

$\begin{matrix}{P_{w,{k + 1}} = {{\frac{1}{C_{w}R_{p}}( {{( {R_{P} + Z_{0}} )Q_{CO}} - P_{{CO},k}} )\delta\; t} + P_{w,k}}} & (2) \\{P_{{ao},{k + 1}} = {P_{w,{k + 1}} + {Z_{0}Q_{CO}}}} & (3)\end{matrix}$where R_(p) and Z_(o) are the peripheral resistance and characteristicaortic impedance, respectively. The sum of these two terms is the totalperipheral resistance due to viscous (Poiseuille-like) dissipationaccording to equation 4,Z ₀=√{square root over (ρ/AC _(l))}  (4)where ρ is blood density and C_(l) is the compliance per unit length ofartery. The elastic component due to vessel compliance is a nonlinearfunction including thoracic aortic cross-sectional area, A: according toequation 5,

$\begin{matrix}{{A( P_{CO} )} = {A_{\max}\lbrack {\frac{1}{2} + {\frac{1}{\pi}{\arctan( \frac{P_{CO} - P_{0}}{P_{1}} )}}} \rbrack}} & (5)\end{matrix}$where A_(max), P₀, and P₁ are fitting constants correlated with age andgender according to equations 6-8.A _(max)=(5.62−1.5(gender))·cm²  (6)P ₀=(76−4(gender)−0.89(age))·mmHg  (7)P ₁(57−0.44(age))·mmHg  (8)

The time-varying Windkessel compliance, C_(w), and the aortic complianceper unit length, C_(l), are related in equation 9,

$\begin{matrix}{C_{w} = {{lC}_{l} = {{l\;\frac{\mathbb{d}A}{\mathbb{d}P_{\infty}}} = {l\frac{\;{A_{\max}/( {\pi\; P_{1}} )}}{1 + ( \frac{P_{\infty} - P_{0}}{P_{1}} )}}}}} & (9)\end{matrix}$where l is the aortic effective length. The peripheral resistance isdefined as the ratio of average pressure to average flow. A set-pointpressure, P_(set), and the instantaneous flow related to the peripheralresistance, R_(p), according to equation 10,

$\begin{matrix}{R_{P} = \frac{P_{set}}{( {{HR} \cdot {SV}} )/60}} & (10)\end{matrix}$are used to provide compensation to autonomic nervous system responses.The value for P_(set) is optionally adjusted manually to obtain 120 over75 mmHg for a healthy individual at rest.Light Scattering and Absorbance Model

The light scattering and absorbance model 816 of the hemodynamicsdynamic state-space model 805 is further described. The compliance ofblood vessels changes the interactions between light and tissues withpulse. This is accounted for using a homogenous photon diffusion theoryfor a reflectance or transmittance pulse oximeter configurationaccording to equation 11,

$\begin{matrix}{R = {\frac{I_{\;{a\; c}}}{I_{d\; c}} = {\frac{\Delta\; I}{I} = {\frac{3}{2}{\overset{1}{\sum\limits_{s}}{{K( {\alpha,d,r} )}{\overset{art}{\sum\limits_{a}}{\Delta\; V_{0}}}}}}}}} & (11)\end{matrix}$for each wavelength. In this example, the red and infrared bands arecentered at about 660±100 nm and at about 880±100 nm. In equation 11, l(no subscript) denotes the detected intensity, R, is the reflectedlight, and the, l_(ac), is the pulsating or ac intensity or signal,l_(ds), is the background or dc intensity, α, is the attenuationcoefficient, d, is the illumination length scale or depth of photonpenetration into the skin, and, r, is the distance between the sourceand detector.

Referring again to the vascular model 814, V_(a) is the arterial bloodvolume, which changes as the cross-sectional area of illuminated bloodvessels, ΔA_(w), according to equation 12,ΔV _(a) ≈r·ΔA _(w)  (12)where r is the source-detector distance.

Referring again to the light scattering and absorbance model 816, thetissue scattering coefficient, Σ_(s)′, is assumed constant but thearterial absorption coefficient, Σ_(a) ^(art), which represents theextinction coefficients, depends on blood oxygen saturation, SpO₂,according to equation 13,

$\begin{matrix}{\overset{art}{\sum\limits_{a}}{= {\frac{H}{v_{i}}\lbrack {{{SpO}_{2} \cdot \sigma_{0}^{100\%}} + {( {1 - {SpO}_{2}} ) \cdot \sigma_{0}^{0\%}}} \rbrack}}} & (13)\end{matrix}$which is the Beer-Lambert absorption coefficient, with hematocrit, H,and red blood cell volume, v_(i). The optical absorption cross-sections,proportional to the absorption coefficients, for red blood cellscontaining totally oxygenated (HbO₂) and totally deoxygenated (Hb)hemoglobin are σ_(a) ^(100%) and σ_(a) ^(0%), respectively.

The function K(α, d, r), along with the scattering coefficient, thewavelength, sensor geometry, and oxygen saturation dependencies, altersthe effective optical pathlengths, according to equation 14.

$\begin{matrix}{{K( {\alpha,d,r} )} \approx \frac{- r^{2}}{1 + {\alpha\; r}}} & (14)\end{matrix}$

The attenuation coefficient α is provided by equation 15,α=√{square root over (3Σ_(a)(Σ_(s)+Σ_(a)))}  (15)where Σ_(a) and Σ_(s) are whole-tissue absorption and scatteringcoefficients, respectively, which are calculated from Mie Theory.

Red, K_(r) , and infrared, K_(ir) , K values as a function of SpO₂ areoptionally represented by two linear fits, provided in equations 16 and17K _(r) ≈−4.03·SpO₂−1.17  (16)K _(ir) ≈0.102·SpO₂−0.753  (17)in mm². The overbar denotes the linear fit of the original function.Referring yet again to the vascular model 814, the pulsatile behavior ofΔA_(w), which couples optical detection with the cardiovascular systemmodel, is provided by equation 18,

$\begin{matrix}{{\Delta\; A_{w}} = {\frac{A_{w,\max}}{\pi}\frac{P_{w,1}}{P_{w,1}^{2} + ( {P_{w,{k + 1}} - P_{w,0}} )^{2}}\Delta\; P_{w}}} & (18)\end{matrix}$with P_(w,0)=(⅓)P₀ and P_(w,1)=(⅓)P₁ to account for the poorercompliance of arterioles and capillaries relative to the thoracic aorta.The subscript k is a data index and the subscript k+1 or k+n refers tothe next or future data point.

Referring yet again to the light scattering and absorbance models, thirdand fourth state variables, the red and infrared reflected intensityratios, R=I_(ac)/I_(dc), are provided by equations 19 and 20.R _(r,k+1) =cΣ′ _(s,r) K _(r) Σ_(a,r) ^(art) ΔA _(w) +R_(r,k)+ν_(r)  (19)R _(ir,k+1) =cΣ′ _(s,ir) K _(ir) Σ_(a,ir) ^(art) ΔA _(w) +R_(ir,k)+ν_(ir)  (20)

Here, ν is a process noise, such as an added random number or areGaussian-distributed process noises intended to capture the baselinewander of the two channels, Σ′_(s,r) and Σ′_(s,ir) are scatteringcoefficients, and Σ_(a,r) ^(art) and Σ_(a,ir) ^(art) are absorptioncoefficients.

Sensor Dynamics and Noise Model

The sensor dynamics and noise model 822 is further described. Theconstant c subsumes all factors common to both wavelengths and istreated as a calibration constant. The observation model adds noises, n,with any probability distribution function to R_(r) and R_(ir),according to equation 21.

$\begin{matrix}{\begin{bmatrix}y_{r,k} \\y_{{ir},k}\end{bmatrix} = {\begin{bmatrix}R_{r,k} \\R_{{ir},k}\end{bmatrix} + \begin{bmatrix}n_{r,k} \\n_{{ir},k}\end{bmatrix}}} & (21)\end{matrix}$

A calibration constant, c, was used to match the variance of the reall_(ac)/l_(dc) signal with the variance of the dynamic state-space modelgenerated signal for each wavelength. After calibration, the age andgender of the patient was entered. Estimates for the means andcovariances of both state and parameter PDFs are optionally entered.

Referring now to FIG. 9, processed data from a relatively highsignal-to-noise ratio pulse oximeter data source is provided for afifteen second stretch of data. Referring now to FIG. 9A, inputphotoplethysmographic waveforms are provided. Using the hemodynamicsdynamic state-space model 805, the input waveforms were used to extractheart rate (FIG. 9B), left-ventricular stroke volume (FIG. 9C), cardiacoutput (FIG. 9D), blood oxygen saturation (FIG. 9E), and aortic andsystemic (radial) pressure waveforms (FIG. 9F). Several notable pointsare provided. First, the pulse oximeter provided a first physical valueof a hemoglobin oxygen saturation percentage. However, the output bloodoxygen saturation percentage, FIG. 9E, was processed by theprobabilistic digital signal processor 200. Due to the use of the sensordynamics and noise model 822 and the spectrometer signal transductionnoise model, noisy data, such as due to ambulatory movement of thepatient, is removed in the smoothed and filtered output blood oxygensaturation percentage. Second, some pulse oximeters provide a heartrate. However, in this case the heart rate output was calculated usingthe physical probabilistic digital signal processor 200 in the absenceof a heart rate input data source 122. Third, each of the stroke volume,FIG. 9C, cardiac output flow rate, FIG. 9D, aortic blood pressure, FIG.9E, and radial blood pressure, FIG. 9E, are second physical parametersthat are different from the first physical parameter measured by thepulse oximeter photoplethysmographic waveforms.

Referring now to FIG. 10, a second stretch of photoplethysmographicwaveforms are provided that represent a low signal-to-noise ratio signalfrom a pulse oximeter. Low signal-to-noise photoplethysmographicwaveforms (FIG. 10A) were used to extract heart rate (FIG. 10B),left-ventricular stroke volume (FIG. 10C), blood oxygen saturation (FIG.10D), and aortic and systemic (radial) pressure waveforms (FIG. 10E)using the hemodynamics dynamic state-space model 805. In each case, theuse of the probabilistic digital signal processor 200 configured withthe optional sensor dynamics and noise model 822 and spectrometer signaltransduction model 824 overcame the noisy input stream to yield smoothand functional output data for medical use.

The variable models relate first measured parameters, such as a pulseoxygen level, to additional model terms, such as a stroke volume.

Electrocardiography

Electrocardiography is a noninvasive transthoracic interpretation of theelectrical activity of the heart over time as measured by externallypositioned skin electrodes. An electrocardiographic device produces anelectrocardiogram (ECG or EKG).

The electrocardiographic device operates by detecting and amplifying theelectrical changes on the skin that are caused when the heart muscledepolarizes, such as during each heartbeat. At rest, each heart musclecell has a charge across its outer wall, or cell membrane. Reducing thischarge towards zero is called de-polarization, which activates themechanisms in the cell that cause it to contract. During each heartbeata healthy heart will have an orderly progression of a wave ofdepolarization that is triggered by the cells in the sinoatrial node,spreads out through the atrium, passes through intrinsic conductionpathways, and then spreads all over the ventricles. The conduction isdetected as increases and decreases in the voltage between twoelectrodes placed on either side of the heart. The resulting signal isinterpreted in terms of heart health, function, and/or weakness indefined locations of the heart muscles.

Examples of electrocardiograph device lead locations and abbreviationsinclude:

-   -   right arm (RA);    -   left arm (LA);    -   right leg (RL);    -   left leg (LL);    -   in fourth intercostal space to right of sternum (V₁);    -   in fourth intercostal space to left of the sternum (V₂);    -   between leads V₂ and V₄ (V₃);    -   in the fifth intercostal space in the mid clavicular line (V₄);    -   horizontally even with V₄, but in the anterior axillary line        (V₅); and    -   horizontally even with V₄ and V₅ in the midaxillary line (V₆).

Usually more than two electrodes are used and they are optionallycombined into a number of pairs. For example, electrodes placed at theleft arm, right arm, and left leg form the pairs LA+RA, LA+LL, andRA+LL. The output from each pair is known as a lead. Each lead examinesthe heart from a different angle. Different types of ECGs can bereferred to by the number of leads that are recorded, for example3-lead, 5-lead or 12-lead ECGs.

Electrocardiograms are used to measure and diagnose abnormal rhythms ofthe heart, such as abnormal rhythms caused by damage to the conductivetissue that carries electrical signals or abnormal rhythms caused byelectrolyte imbalances. In a myocardial infarction (MI) or heart attack,the electrocardiogram is used to identify if the heart muscle has beendamaged in specific areas. Notably, traditionally an ECG cannot reliablymeasure the pumping ability of the heart, for which additional tests areused, such as ultrasound-based echocardiography or nuclear medicinetests. Along with other uses of an electrocardiograph model, theprobabilistic mathematical electrocardiograph model, described infra,shows how this limitation is overcome.

EXAMPLE II

A second example of a dynamic state-space model 210 coupled with a dualor joint estimator 222 and/or a probabilistic updater 220 orprobabilistic sampler 230 in a medical or biomedical application isprovided.

Ischemia and Heart Attack

For clarity, a non-limiting example of prediction of ischemia using anelectrocardiograph dynamic state-space model is provided. A normal hearthas stationary and homogenous myocardial conducting pathways. Further, anormal heart has stable excitation thresholds resulting in consecutivebeats that retrace with good fidelity. In an ischemic heart, conductancebifurcations and irregular thresholds give rise to discontinuouselectrophysiological characteristics. These abnormalities have subtlemanifestations in the electrocardiograph morphology that persist longbefore shape of the electrocardiograph deteriorates sufficiently toreach detection by a skilled human operator. Ischemic abnormalities arecharacterized dynamically by non-stationary variability between heartbeats, which are difficult to detect, especially when masked by highfrequency noise, or similarly non-stationary artifact, such as electrodelead perturbations induced by patient motion.

Detection performance is improved substantially relative to the bestpractitioners and current state-of-the-art algorithms by integrating amathematical model of the heart with accurate and rigorous handling ofprobabilities. An example of an algorithm for real time and near-optimalECG processing is the combination of a sequential Monte Carlo algorithmwith Bayes rule. Generally, an electrodynamic mathematical model of theheart with wave propagation through the body is used to provide a‘ground truth’ for the measured signal from the electrocardiographelectrode leads. Use of a sequential Monte Carlo algorithm predicts amultiplicity of candidate values for the signal, as well as other healthstates, at each time point, and each is used as a prior to calculate thetruth estimate based on sensor input via a Bayesian update rule. Sincethe model is electrodynamic and contains state and model parametervariables corresponding to a normal condition and an ischemic condition,such events can be discriminated by the electrocardiograph model,described infra.

Unlike simple filters and algorithms, the electrocardiograph dynamicstate-space model coupled with the probabilistic updater 220 orprobabilistic sampler 230 is operable without the use of assumptionsabout the regularity of morphological variation, spectra of noise orartifact, or the linearity of the heart electrodynamic system. Instead,the dynamic response of the normal or ischemic heart arises naturally inthe context of the model during the measurement process. The accurateand rigorous handling of probabilities of this algorithm allows thelowest possible detection limit and false positive alarm rate at anylevel of noise and/or artifact corruption.

Electrocardiograph with Probabilistic Data Processing

FIG. 11 is a schematic of an electrocardiograph dynamic state-spacemodel suitable for processing electrocardiogram data, includingcomponents required to describe the processes occurring in a subject.The combination of SPKF or SMC filtering in state, joint, or dualestimation modes is optionally used to filter electrocardiography (ECG)data. Any physiology model adequately describing the ECG signal can beused, as well as any model of noise and artifact sources interfering orcontaminating the signal. One non-limiting example of such a model is amodel using a sum of arbitrary wave functions with amplitude, center andwidth, respectively, for each wave (P, Q, R, S, T) in an ECG. Theobservation model comprises the state plus additive Gaussian noise, butmore realistic pink noise or any other noise probability distributionsis optionally used.

Still referring to FIG. 11, to facilitate description of theelectrocardiograph dynamic state-space model 1105, a non-limitingexample is provided. In this example, the electrocardiograph dynamicstate-space model 1105 is further described. The electrocardiographdynamic state-space model 1105 preferably includes a heartelectrodynamics model 1110 corresponding to the dynamic state spacemodel 210 process model 710. Further, the electrocardiograph dynamicstate-space model 1105 preferably includes a heart electrodynamicsobservation model 1120 corresponding to the dynamic state space model210 observation model 720. The electrocardiograph process model 1110 andelectrocardiogram observation model 1120 are further described, infra.

Still referring to FIG. 11, the electrocardiograph process model 1110optionally includes one or more of a heart electrodynamics model 1112and a wave propagation model 1114. The heart electrodynamics 1112 is aphysics based model of the electrical output of the heart. The wavepropagation model 1114 is a physics based model of movement of theelectrical pulses through the lungs, fat, muscle, and skin. An exampleof a wave propagation model 1114 is a thorax wave propagation modelmodeling electrical wave movement in the chest, such as through anorgan. The various models optionally share information. For example, theelectrical pulse of the heart electrodynamics model 1112 is optionallyan input to the wave propagation model 1114, such as related to one ormore multi-lead ECG signals. Generally, the process model 710 componentsare optionally probabilistic, but are preferentially deterministic.Generally, the observation model 720 components are probabilistic.

Still referring to FIG. 11, the electrocardiogram observation model 1120optionally includes one or more of a sensor noise and interference model1122, a sensor dynamics model 1124, and/or an electrode placement model1126. Each of the sensor noise and interference model 1122 and thesensor dynamics models 1124 are optionally physics based probabilisticmodels related to noises associated with the instrumentation used tocollect data, environmental influences on the collected data, and/ornoise due to the human interaction with the instrumentation, such asmovement of the sensor. A physics based model uses at least one equationrelating forces, electric fields, pressures, or light intensity tosensor provided data. The electrode placement model 1126 relates toplacement of the electrocardiograph leads on the body, such as on thearm, leg, or chest. As with the electrocardiograph process model 1110,the sub-models of the electrocardiograph observation model 1120optionally share information. For instance, a first source of noise,such as sensor noise related to movement of the sensor, is added to asecond source of noise, such as a signal transduction noise. Optionallyand preferably, the electrocardiograph observation model 1120 sharesinformation with and/provides information to the electrocardiographprocess model 1110.

The electrocardiograph dynamic state-space model 1105 receives inputs,such as one or more of:

-   -   electrocardiograph state parameters 1130;    -   electrocardiograph model parameters 1140;    -   electrocardiograph process noise 1150; and    -   electrocardiograph observation noise 1160.

Examples of electrocardiograph state parameters 1130, corresponding tostate parameters 730, include: atrium signals (AS), ventricle signals(VS) and/or an ECG lead data. Examples of electrocardiograph modelparameters 1140, corresponding to the more generic model parameters 740,include: permittivity, ε, autonomic nervous system (ANS) tone orvisceral nervous system, and heart rate variability (HRV). Heart ratevariability (HRV) is a physiological phenomenon where the time intervalbetween heart beats varies and is measured by the variation in thebeat-to-beat interval. Heart rate variability is also referred to asheart period variability, cycle length variability, and RR variability,where R is a point corresponding to the peak of the QRS complex of theelectrocardiogram wave; and RR is the interval between successive RS. Inthis example, the output of the electrocardiograph dynamic state-spacemodel 1105 is a prior probability distribution function with parametersof one or more of the input electrocardiograph state parameters 1130after operation on by the heart electrodynamics model 1112, a staticnumber, a probability function and/or a parameter not measured or outputby the sensor data.

An example of an electrocardiograph with probabilistic data processingis provided as an example of the electrocardiogram dynamic state-spacemodel 1105. The model is suitable for processing data from anelectrocardiograph. In this example, particular equations are used tofurther describe the electrocardiograph dynamic state-space model 1105,but the equations are illustrative and non-limiting in nature.

Heart Electrodynamics

The heart electrodynamics model 1112 of the ECG dynamic state-spacemodel 1105 is further described. The transmembrane potential wavepropagation in the heart is optionally simulated using FitzHugh-Nagumoequations. This can be implemented, for instance, on a coarse-grainedthree-dimensional heart anatomical model or a compartmental,zero-dimensional model of the heart. The latter could take the form, forinstance, of separate atrium and ventricle compartments.

In a first example of a heart electrodynamics model, a first set ofequations for cardiac electrodynamics are provided by equations 22 and23,

$\begin{matrix}{\overset{.}{u} = {{{div}( {D\;{\nabla\; u}} )} + {{{ku}( {1 - u} )}( {u - a} )} - {uz}}} & (22) \\{\overset{.}{z} = {{- ( {e + \frac{u_{1}z}{u + u_{2}}} )}( {{{ku}( {u - a - 1} )} + z} )}} & (23)\end{matrix}$where D is the conductivity, u is a normalized transmembrane potential,and z is a secondary variable for the repolarization. In thecompartmental model, u_(i) becomes either the atrium or the ventriclepotential, u_(as) or u_(vs). The repolarization is controlled by k ande, while the stimulation threshold and the reaction phenomenon iscontrolled by the value of a. The parameters ₁ and ₂ are preferablyempirically fitted.

A second example of a heart electrodynamics model is presented, whichthose skilled in the art will understand is related to the first heartelectrodynamics model. The second heart electrodynamics model isexpanded to include a restitution property of cardiac tissue, whererestitution refers to a return to an original physical condition, suchas after elastic deformation of heart tissue. The second heartelectrodynamics model is particularly suited to whole heart modeling andis configured for effectiveness in computer simulations or models.

The second heart electrodynamics model includes two equations, equations24 and 25, describing fast and slow processes and is useful inadequately representing the shape of heart action potential,

$\begin{matrix}{\frac{\partial u}{\partial t} = {{\frac{\partial}{\partial x_{i\;}}d_{ij}\frac{\partial u}{\partial x_{j}}} - {{{ku}( {u - a} )}( {u - 1} )} - {uv}}} & (24) \\{\frac{\partial v}{\partial t} = {ɛ\;( {u,v} )( {{- v} - {{ku}( {u - a - 1} )}} )}} & (25)\end{matrix}$where ε(u,ν)=ε₀+u₁ν/(u+u₂). Herein, the approximate values of k=8,a=0.15, and ε₀=0.002 are used, but the values are optionally set for aparticular model. The parameters u₁ and u₂ are set for a given model andd_(ij) is the conductivity tensor accounting for the heart tissueanisotropy.

Further, the second heart electrodynamics model involves dimensionlessvariables, such as u, v, and t. The actual transmembrane potential, E,and time, t, are obtained using equations 26 and 27 or equivalentformulas.e[mV]=100u−80  (26)t[ms]=12.9t[t.u.]  (27)

In this particular case, the rest potential E_(rest) is about −80 mV andthe amplitude of the pulse is about 100 mV. Time was scaled assuming aduration of the action potential, APD, measured at the level of aboutninety percent of repolarization, APD₀=330 ms. The nonlinear functionfor the fast variable u optionally has a cubic shape.

The dependence of ε on u and v allows the tuning of the restitutioncurve to experimentally determined values using u₁ and u₂. The shape ofthe restitution curve is approximated by equation 28,

$\begin{matrix}{{A\; P\; D} = \frac{CL}{( {{aCL} + b} )}} & (28)\end{matrix}$where the duration of the action potential, APD, is related to the cyclelength, CL. In dimensionless form, equation 28 is rewritten according toequation 29,

$\begin{matrix}{\frac{1}{apd} = {1 + \frac{b}{cl}}} & (29)\end{matrix}$where apd=APD/APD₀, and APD₀ denotes APD of a free propagating pulse.

Restitution curves with varying values of parameters u₁ and u₂ are used,however, optional values for parameters u₁ and u₂ are about u₁=0.2 andu₂=0.3. One form of a restitution curve is a plot of apd vs. cl, or anequivalent. Since a restitution plot using apd vs. cl is a curved line,a linear equivalent is typically preferred. For example, restitutioncurve is well fit by a straight line according to equation 30.

$\begin{matrix}{\frac{1}{apd} = {k_{1} + \frac{k_{2}}{cl}}} & (30)\end{matrix}$

Optional values of k₁ and k₂ are about 1.0 and 1.05, respectively, butare preferably fit to real data for a particular model. Generally, theparameter k₂ is the slope of the line and reflects the restitution atlarger values of CL.

The use of the electrodynamics equations, the restitutions, and/or therestitution curve is subsequently used to predict or measure arrhythmia.Homogeneous output is normal. Inhomogeneous output indicates abifurcation or break in the conductivity of the heart tissue, which hasan anisotropic profile, and is indicative of an arrhythmia. Hence, theslope or shape of the restitution curve is used to detect arrhythmia.

Wave Propagation

The electric wave model 1114 of the ECG dynamic state-space model 1105is further described. The propagation of the heart electrical impulsethrough lung and other tissues before reaching the sensing electrodes isoptionally calculated using Gauss' Law:

$\begin{matrix}{{\nabla{\cdot {E(t)}}} = \frac{u_{i}(t)}{ɛ_{0}}} & (31)\end{matrix}$where _(i)(t) is the time-varying charge density given by the heartelectrodynamics model and ε₀ is the permittivity of free space, which isoptionally scaled to an average tissue permittivity.Sensor Dynamics

The sensor dynamics model 1124 of the ECG dynamic state-space model 1105is further described. The ECG sensor is an electrode that is usuallyinterfaced by a conducting gel to the skin. When done correctly, thereis little impedance from the interface and the wave propagates toward avoltage readout. The overall effect of ancillary electronics on themeasurement should be small. The relationship between the wave andreadout can be written in general as:V(t)=G(E(t))+N(p)+D(s,c)  (32)where G is the map from the electrical field reaching the electrode andvoltage readout. This includes the effect of electronics and electroderesponse timescales, where N is the sensor noise and interference modeland D is the electrode placement model.Sensor Noise and Interference Model

The sensor noise and interference model 1122 of the ECG dynamicstate-space model 1105 is further described. The sensor noise enters theDSSM as a stochastic term (Langevin) that is typically additive but witha PDF that is both non-Gaussian and non-stationary. We modelnon-stationarity from the perturbation, p, representing both externalinterference and cross-talk. One way to accomplish this is to write:N(E(t),p)=αn ₁ +βpn ₂  (33)where alpha, α, and beta, β, are empirical constants, and n₁ and n₂ arestochastic parameters with a given probability distribution function.Electrode Placement Model

The electrode placement model 1126 of the ECG dynamic state-space model1105 is further described. This model is an anatomical correction termto the readout equation operating on the sagittal and coronalcoordinates, s and c, respectively. This model varies significantlybased on distance to the heart and anatomical structures between theheart and sensor. For instance, the right arm placement is vastlydifferent to the fourth intercostal.

Optionally, the output from the electrocardiograph probabilistic modelis an updated, error filtered, or smoothed version of the original inputdata. For example, the probabilistic processor uses a physical modelwhere the output of the model processes low signal-to-noise ratio eventsto yield any of: an arrhythmia detection, arrhythmia monitoring, anearly arrhythmia warning, an ischemia warning, and/or a heart attackprediction.

Optionally, the model compares shape of the ECG with a reference look-uptable, uses an intelligent system, and/or uses an expert system toestimate, predict, or produce one or more of: an arrhythmia detection,an ischemia warning, and/or a heart attack warning.

Referring now to FIG. 12A and FIG. 12B, the results of processing anoisy non-stationary ECG signal are shown. Heart rate oscillationsrepresentative of normal respiratory sinus arrhythmia are present in theECG. The processor accomplishes accurate, simultaneous estimation of thetrue ECG signal and a heart rate that follows closely the true values.Referring now to FIG. 13A and FIG. 13B, the performance of the processorusing a noise and artifact-corrupted signal is shown. A clean ECG signalrepresenting one heart beat was contaminated with additive noise and anartifact in the form of a plateau at R and S peaks (beginning at time=10sec). Estimates by the processor remain close to the true signal despitethe noise and artifact.

Fusion Model

Optionally, inputs from multiple data sources, such as medicalinstruments, are fused using the probabilistic digital signal processor200. The fused data often includes partially overlapping information,which is shared between models or used in a fused model to enhanceparameter estimation. For example, data from two instruments oftenshares or has related modeled information, such as information in one orboth of the process model 710 and the observation model 720.

Pulse Oximeter/ECG Fusion

A non-limiting example of fusion of information from a pulse oximeterand an ECG is used to clarify model fusion and/or informationcombination.

A pulse oximeter and an ECG both provide information on the heart.Hence, the pulse oximeter and the ECG provide overlapping information,which is optionally shared, such as between the hemodynamics dynamicstate-space model 805 and the ECG dynamic state-space model 1105.Similarly, a fused model incorporating aspects of both the hemodynamicsdynamic state-space model 805 and the ECG dynamic state-space model 1105is created, which is an example of a fused model. Particularly, in anECG the left-ventricular stroke volume is related to the power spentduring systolic contraction, which is, in turn, related to theelectrical impulse delivered to that region of the heart. Indeed, theR-wave amplitude is optionally correlated to contractility. It is notdifficult to imagine that other features of the ECG may also have arelationship with the cardiac output function. As described, supra, thepulse oximeter also provides information on contractility, such as heartrate, stroke volume, cardiac output flow rate, and/or blood oxygensaturation information. Since information in common is present, thesystem is over determined, which allow outlier analysis and/orcalculation of a heart state or parameter with increased accuracy and/orprecision.

The above description describes an apparatus for generation of aphysiological estimate of a physiological process of an individual frominput data, where the apparatus includes a biomedical monitoring devicehaving a data processor configured to run a dual estimation algorithm,where the biomedical monitoring device is configured to produce theinput data, and where the input data comprises at least one of: aphotoplethysmogram and an electrocardiogram. The dual estimationalgorithm is configured to use a dynamic state-space model to operate onthe input data using both an iterative state estimator and an iterativemodel parameter estimator in generation of the physiological estimate,where the dynamic state-space model is configured to mathematicallyrepresent probabilities of physiological processes that generate thephysiological estimate and mathematically represent probabilities ofphysical processes that affect collection of the input data. Generally,the algorithm is implemented using a data processor, such as in acomputer, operable in or in conjunction with a biomedical monitoringdevice.

ADDITIONAL EMBODIMENTS

In yet another embodiment, the method, system, and/or apparatus using aprobabilistic model to extract physiological information from abiomedical sensor, described supra, optionally uses a sensor providingtime-dependent signals. More particularly, pulse ox and ECG exampleswere provided, supra, to describe the use of the probabilistic modelapproach. However, the probabilistic model approach is more widelyapplicable.

The above description describes an apparatus for generation of aphysiological estimate of a physiological process of an individual frominput data, where the apparatus includes a biomedical monitoring devicehaving a data processor configured to run a dual estimation algorithm,where the biomedical monitoring device is configured to produce theinput data and where the input data includes at least one of: aphotoplethysmogram and an electrocardiogram. The dual estimationalgorithm is configured to use a dynamic state-space model to operate onthe input data using both an iterative state estimator and an iterativemodel parameter estimator in generation of the physiological estimate,where the dynamic state-space model is configured to mathematicallyrepresent probabilities of physiological processes that generate thephysiological estimate and mathematically represent probabilities ofphysical processes that affect collection of the input data. Generally,the algorithm is implemented using a data processor, such as in acomputer, operable in or in conjunction with a biomedical monitoringdevice.

In yet another embodiment, the method, system, and/or apparatus using aprobabilistic model to extract physiological information from abiomedical sensor, described supra, optionally uses a sensor providingtime-dependent signals. More particularly, pulse ox and ECG exampleswere provided, infra, to describe the use of the probabilistic modelapproach. However, the probabilistic model approach is more widelyapplicable.

Some examples of physiological sensors used for input into the systemwith a corresponding physiological model include:

-   -   an ECG having about two to twelve leads yielding an ECG waveform        used to determine an RR-interval and/or various morphological        features related to arrhythmias;    -   pulse photoplethysmography yielding a PPG waveform for        determination of hemoglobins and/or total hemoglobin;    -   capnography or IR absorption yielding a real time waveform for        carbon dioxide determination, end-tidal CO₂, an inspired        minimum, and/or respiration rate;    -   a temperature sensor for continuous determination of core body        temperature and/or skin temperature;    -   an anesthetic gas including nitrous oxide, N₂O, and carbon        dioxide, CO₂, used to determine minimum alveolar concentration        of an inhaled anesthetic;    -   a heart catheter yielding a thermodilution curve for        determination of a cardiac index and/or a blood temperature;    -   an impedance cardiography sensor yielding a thoracic electrical        bioimpedance reading for determination of thoracic fluid        content, accelerated cardiac index, stroke volume, cardiac        output, and/or systemic vascular resistance;    -   a mixed venous oxygen saturation catheter for determination of        SvO₂;    -   an electroencephalogram (EEG) yielding an EEG waveform and        characteristics thereof, such as spectral edge frequency, mean        dominant frequency, peak power frequency, compressed spectral        array analysis, color pattern display, and/or        delta-theta-alpha-beta band powers, any of which are used for        analysis of cardiac functions described herein;    -   electromyography (EMG) yielding an EMG waveform including        frequency measures, event detection, and/or amplitude of        contraction;    -   auscultation yielding sound pressure waveforms;    -   transcutaneous blood gas sensors for determination of carbon        dioxide, CO₂, and oxygen, O₂;    -   a pressure cuff yielding a pressure waveform for determination        of systolic pressure, diastolic pressure, mean arterial        pressure, heart rate, and/or hemodynamics;    -   spirometry combining capnography and flow waveforms for        information on respiratory rate, tidal volume, minute volume,        positive end-expiratory pressure, peak inspiratory pressure,        dynamic compliance, and/or airway resistance;    -   fetal and/or maternal sensors, such as ECG and sound        (auscultatory) sensors for determination of fetal movement,        heart rate, uterine activity, and/or maternal ECG;    -   laser Doppler flowmetry yielding a velocity waveform for        capillary blood flow rate;    -   an ultrasound and/or Doppler ultrasound yielding a waveform,        such as a two-dimensional or three-dimensional image, for        imaging and/or analysis of occlusion of blood vessel walls,        blood flow velocity profile, and/or other body site dependent        measures;    -   a perspirometer yielding a continuous or semi-continuous surface        impedance for information on skin perspiration levels; and    -   a digital medical history database to calibrate the model or to        screen the database for patient diseases and/or conditions.

Some examples of non-physiological sensors used for input into thesystem with a corresponding physiological model include:

-   -   an accelerometer;    -   a three axes accelerometer;    -   a gyroscope;    -   a compass;    -   light or a light reading;    -   a global positioning system, for air pressure data, ambient        light, humidity, and/or temperature;    -   a microphone; and/or    -   an ambient temperature sensor.

While specific dynamic state-space models and input and outputparameters are provided for the purpose of describing the presentmethod, the present invention is not limited to the examples of thedynamic state-space models, sensors, biological monitoring devices,inputs, and/or outputs provided herein.

Diagnosis/Prognosis

Referring now to FIG. 14, the output of the probabilistic digital signalprocessor 200 optionally is used to diagnose 1410 a system element orcomponent. The diagnosis 1410 is optionally used in a process ofprognosis 1420 and/or in control 1430 of the system.

Although the invention has been described herein with reference tocertain preferred embodiments, one skilled in the art will readilyappreciate that other applications may be substituted for those setforth herein without departing from the spirit and scope of the presentinvention. Accordingly, the invention should only be limited by theClaims included below.

The invention claimed is:
 1. An apparatus for electrodynamic analysis ofa body comprising a heart, the apparatus comprising: a digital signalprocessor integrated into a biomedical device, said digital signalprocessor configured to use: an electrodynamics dynamic state-spacemodel and a probabilistic processor to produce an initial posteriorprobability distribution function using input from both an opticalhemodynamic waveform measurement generated using output from an opticalprobe and an electrodynamic signal from an electrocardiogram of theheart of the body; and a probabilistic updater configured to generate atime varying aortic pressure waveform using all of: (1) iterative inputof a prior probability distribution function, the prior probabilitydistribution function comprising a previous iteration output of aposterior probability distribution function from the electrodynamicsdynamic state-space model, (2) iterative optical hemodynamic waveformmeasurement input generated using the optical probe, and (3) iterativeelectrodynamic signal from the electrocardiogram of the body, whereinsaid electrodynamics dynamic state-space model comprises: a processmodel, wherein said process model comprises a model describing electriccharge transfer in the body.
 2. The apparatus of claim 1, said processmodel further comprising: a heart electrodynamics model.
 3. Theapparatus of claim 1, wherein the electrodynamic signal comprises outputof an electrocardiograph device.
 4. The apparatus of claim 1, saiddigital signal processor configured to generate an output, wherein theoutput comprises a prognosis of a heart attack.
 5. The apparatus ofclaim 1, said digital signal processor configured to generate an output,wherein the output comprises an arrhythmia detection based upon a modelmeasuring contractility.
 6. The apparatus of claim 1, said probabilisticprocessor configured to process the electrodynamic signal using both asequential Monte Carlo algorithm and Bayes rule.
 7. The apparatus ofclaim 1, said process model further comprising: a probabilistic model.8. The apparatus of claim 1, wherein the electrodynamic signal comprisesa deterministic state reading of the body, said probabilistic processorconfigured to convert the deterministic state reading into a probabilitydistribution function, said system processor configured to provide anoutput probability distribution function representative of state ofhealth of the body.
 9. The apparatus of claim 1, wherein theelectrodynamic signal comprises at least one of: raw sensor data relatedto a first physical parameter; and an output related to a providedphysical parameter, wherein output correlated with the posteriorprobability distribution function relates to a second physical parametercalculated using said process model, wherein the second physicalparameter is to a physical parameter other than the first physicalparameter and the provided physical parameter.
 10. The apparatus ofclaim 1, said process model of said dynamic state-space model furthercomprising: a physics based model configured to represent movement ofthe electrodynamic signal in at least a chest of the body.
 11. A methodfor electrodynamic analysis of a body comprising a heart, the methodcomprising the steps of: providing a digital signal processor integratedinto a biomedical device, said digital signal processor configured touse: an electrodynamics dynamic state-space model; and a probabilisticprocessor; said probabilistic processor producing an initial posteriorprobability distribution function using input from both aphotoplethysmogram signal generated using output from an optical probeand an electrodynamic signal from an electrocardiogram of the heart ofthe body; a probabilistic updater generating a time varying aorticpressure waveform using all of: (1) iterative input of a priorprobability distribution function, the prior probability distributionfunction comprising a previous iteration output of a posteriorprobability distribution function from the electrodynamics dynamicstate-space model, (2) iterative optical photoplethysmographic signalgenerated using the optical probe, and (3) iterative electrodynamicsignal originating in the heart of the body, wherein saidelectrodynamics dynamic state-space model comprises: a process modelrelating both the photoplethysmogram signal and the electrodynamicsignal originating in the body to systolic contraction.
 12. The methodof claim 11, further comprising the step of: fusing the electrodynamicssignal generated with a first sensor with a second data stream generatedusing a second sensor, wherein the second data stream relates to ahemodynamics process.
 13. The method of claim 11, said electrodynamicsdynamic state-space model further comprising the step of: an electricalwave propagation model modeling an electric charge moving at least in achest of the body.
 14. The method of claim 11, said process modelfurther comprising the step of: using a physical model to relate theelectrodynamics signal with any of: a heart atrium; and a heartventricle.
 15. The method of claim 11, said process model furthercomprising the step of: using said process model to represent at least aportion of a heart action potential.
 16. The method of claim 11, whereinsaid process model comprises use of a model relating duration of a heartaction potential to a heartbeat cycle length.
 17. The method of claim11, wherein the electrodynamic signal comprises at least one of: rawsensor data related to a first physical parameter; and an output relatedto a provided first physical parameter, wherein output correlated withthe posterior probability distribution function relates to a secondphysical parameter calculated using said process model, wherein thesecond physical parameter is to a physical parameter other than thefirst physical parameter and the provided physical parameter.
 18. Themethod of claim 17, wherein said prior probability distribution functioncomprises a distribution of at least one of: voltage values; currentvalues; electrical impedances; and electrical resistance values.
 19. Amethod for electrodynamic analysis of a heart of a body, comprising thesteps of: providing a digital signal processor integrated into abiomedical device, said digital signal processor producing an initialposterior probability distribution function using input from (1) aphotoplethysmogram and (2) a probability distribution function using aphysical model representative of a compartment of the heart of the body;a probabilistic updater, of said digital processor, subsequentlygenerating a time varying aortic pressure waveform using all of: (1)iterative input of a prior probability distribution function, the priorprobability distribution function comprising a previous iteration outputof a posterior probability distribution function generated using thephysical model, (2) iterative input from the photoplethysmogram, and (3)iterative electrodynamic signal originating in the body, wherein saidphysical model comprises: a process model configured to: model electriccharge transfer in the heart; and use at least one equation relating aheart contraction state to at least one of: an atrium potentialvariable; a ventricle potential variable.
 20. The method of claim 19,said biomedical device configured to provide a probabilistic outputrepresentative of state of a heart of the body.
 21. The method of claim19, said biomedical device configured to provide an output, said outputcomprising a measure of heart rate variability.